How many #3d_(z^2)# orbitals have #n = 3# and #l = 2#?

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Answer 1 · 2016-11-09T06:26:05

You already specified an orbital, so... one...

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The #3d_(z^2)# is the specific orbital with:

#bb(n = 3)#, because the #3# in front says that. Thus, it is in the 3rd quantum level.
#bb(l = 2)#, which corresponds to a #d# orbital, since the values of #l# correspond as #(0,1,2,3,4, . . . ) harr (s,p,d,f,g, . . . )#.
#m_l# for this orbital is one of the values in the following set: #{-2,-1,0,+1,+2}#. It does not matter which one, but it is only one of them, since you have specified only one #d# orbital. That is, #m_l# is known, but is yours to choose, since all the #3d# orbitals in an atom are the same energy (degenerate).
#m_s# requires more information to specify, but it can either be #pm"1/2"# in general. It depends on how many electrons were in that orbital to begin with, whether it's spin-up or spin-down for the electron of choice.